For an hour or so on Monday at the Leveson inquiry, former cabinet secretary Gus O'Donnell delivered a masterclass in the skills of discretion and gentle evasion that took him to the top of the civil service; not for him the Murdochian pauses or premature dementia favoured by some witnesses.

So it was striking when a question about the security vetting of Downing Street press secretaries left him momentarily lost for words. Robert Jay, counsel to the inquiry, wanted to know if Andy Coulson's predecessors had been subjected to so-called developed vetting (DV), the level of scrutiny which allows people to see top secret documents without supervision.

O'Donnell, often referred to in Whitehall as GOD for more reasons than his initials, gave a brief impression of a goldfish before replying: "It's a question of what you define as the post, but I think in general terms they – well, I'm just trying to think who would have been the equivalent before."

Until recently the issue of Coulson's security status has been something of a minority sport, even among close students of the three-year hacking saga. Put simply, it boils down to the question: why was he subjected to less strenuous security vetting than most (perhaps all) of his predecessors?

When it emerged last July that Coulson was cleared only to the relatively low SC level, a number of senior former No 10 staff expressed bafflement. It was absolutely standard practice for press secretaries to be DV cleared, they said, a view echoed by Alastair Campbell in his own Leveson evidence today. One former holder of the post said it would have been impossible to do his job without it. Since then several senior military and police figures have privately told the Guardian they were shocked to discover Coulson had not been properly vetted.

For months, Downing Street has responded to questions on the subject with increasingly tetchy variations on the old policeman's refrain: "Move along, nothing to see here." The lower level of vetting was approved by the (then) permanent secretary, Jeremy Heywood; only a handful of advisers were DV cleared; Coulson never saw papers that he shouldn't have.

Last week Coulson himself made a most unhelpful disclosure. Asked at the Leveson inquiry whether he had had unsupervised access to material classified top secret or above, he replied "I may have done, yes." The phrase was key because it is the definition of the level of access for which more strenuous DV vetting is required.Downing Street had pointedly refused to use it before.

To make matters worse Coulson added that he had also attended meetings of the national security council.

On Monday, a palpably uncomfortable O'Donnell offered a series of halfhearted explanations for Coulson's anomalous treatment. Press secretaries might need to be DV vetted during periods when they would be expected to deal with sensitive subjects such as "when you're at war". But not the kind of war Britain was involved in in Afghanistan, evidently.

There was some misunderstanding of what DV vetting actually involves, he said. It wouldn't "have gone into enormous detail about phone hacking" but investigates "whether you're blackmailable, basically". But not whether you are blackmailable about previous involvement in tabloid dirty tricks.

Does it really matter what level of security vetting Coulson underwent? After all, nobody is suggesting that he photocopied top secret plans for the pullout from Afghanistan and slipped them to his old chums at the News of the World.There may be an innocent explanation for the decision not to vet him at the same level as his predecessors, despite the multiple warnings and dozens of newspaper reports about his alleged involvement with tabloid dark arts, but the trouble is that Occam's razor points away from it: quite simply it is more plausible that the prime minister or his staff chose not to look too closely for fear of what they might find.

If No 10 wants to prove, as Leveson suggested, that "there isn't a smoking gun here", it will have to give a more convincing – and complete – explanation than it has managed so far.